Given: Angle L N O ≅ Angle L N M Angle O L N ≅ Angle M L N Prove: Angle L N O ≅ Angle L N M Triangles L O N and L M N share common side L N. Angles O L N and N L M are congruent. Angles O N L and L N M are congruent. It is given that angle LNO is congruent to angle and angle OLN is congruent to angle . We know that side LN is congruent to side LN because of the . Therefore, because of , we can state that triangle LNO is congruent to triangle LNM.

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levicade12 levicade12 · Answer 1 · 2020-11-05T16:32:56+01:00

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oeerivona oeerivona · Answer 2 · 2021-11-14T15:41:06+01:00

ΔLNO and ΔLNM have a pair of congruent corresponding angles and

share the included side between the angles.

The two column proof is presented as follows;

Statement [tex]{}[/tex] Reason:

1. ∠LNO ≅ ∠LNM [tex]{}[/tex] 1. Given

2. ∠OLN ≅ ∠MLN [tex]{}[/tex] 2. Given

3. [tex]\overline{LN}[/tex] ≅ [tex]\overline{LN}[/tex] [tex]{}[/tex] 3. Reflexive property

4. ΔLNO ≅ ΔLNM [tex]{}[/tex] 4. ASA rule of congruency

Reasons:

The acronym, ASA stands for Angle-Side-Angle, rule of congruency, which

states that two triangles are congruent, if two angles and the included side

of one triangle are congruent to to angles and the included side of the

other triangle.

The given parameters include two angles on triangle ΔLNO, which are

congruent to the corresponding two angles on triangle ΔLNM.

The two triangles share a common side, [tex]\overline{LN}[/tex], and by reflexive property, the

side, [tex]\overline{LN}[/tex] on both triangles are congruent.

Therefore, by ASA rule of congruency, ΔLNO is congruent to ΔLNM

(ΔLNO ≅ ΔLNM).

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